The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation | Zendy

Olivier Bournez | Zendy; Manuel L. Campagnolo | Zendy; Daniel S. Graça | Zendy; Emmanuel Hainry | Zendy

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The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation

Author(s) -

Olivier Bournez,

Manuel L. Campagnolo,

Daniel S. Graça,

Emmanuel Hainry

Publication year - 2006

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-34021-1

DOI - 10.1007/11750321_60

Subject(s) - computable analysis , computable number , computable function , analog computer , computability , computation , computer science , algebra over a field , computability theory , polynomial , computable general equilibrium , theoretical computer science , algorithm , mathematics , pure mathematics , mathematical analysis , electrical engineering , engineering , economics , macroeconomics

In this paper we revisit one of the first models of analog computation, Shannon’s General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPAC-computability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial differential equations then we show that all real computable functions can be defined by such models.

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